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Potential energy

  1. A tennis ball, of mass 120 g , is dropped from a height of 5 m . Ignore air friction.
    1. What is the potential energy of the ball when it has fallen 3 m ?
    2. What is the velocity of the ball when it hits the ground?
  2. A bullet, mass 50 g , is shot vertically up in the air with a muzzle velocity of 200 m · s - 1 . Use the Principle of Conservation of Mechanical Energy to determine the height that the bullet will reach. Ignore air friction.
  3. A skier, mass 50 kg , is at the top of a 6,4 m ski slope.
    1. Determine the maximum velocity that she can reach when she skies to the bottom of the slope.
    2. Do you think that she will reach this velocity? Why/Why not?
  4. A pendulum bob of mass 1,5 kg , swings from a height A to the bottom of its arc at B. The velocity of the bob at B is 4 m · s - 1 . Calculate the height A from which the bob was released. Ignore the effects of air friction.
  5. Prove that the velocity of an object, in free fall, in a closed system, is independent of its mass.

Energy graphs

Let us consider our example of the suitcase on the cupboard, once more.

Let's look at each of these quantities and draw a graph for each. We will look at how each quantity changes as the suitcase falls from the top to the bottom of the cupboard.

  • Potential energy : The potential energy starts off at a maximum and decreases until it reaches zero at the bottom of the cupboard. It had fallen a distance of 2 metres.
  • Kinetic energy : The kinetic energy is zero at the start of the fall. When the suitcase reaches the ground, the kinetic energy is a maximum. We also use distance on the x -axis.
  • Mechanical energy : The mechanical energy is constant throughout the motion and is always a maximum. At any point in time, when we add the potential energy and the kinetic energy, we will get the same number.

The following presentation provides a summary of some of the concepts covered in this chapter.

Summary

  • Mass is the amount of matter an object is made up of.
  • Weight is the force with which the Earth attracts a body towards its centre.
  • Newtons Law of Gravitation.
  • A body is in free fall if it is moving in the Earth's gravitational field and no other forces act on it.
  • The equations of motion can be used for free fall problems. The acceleration (a) is equal to the acceleration due to gravity (g).
  • The potential energy of an object is the energy the object has due to his position above a reference point.
  • The kinetic energy of an object is the energy the object has due to its motion.
  • Mechanical energy of an object is the sum of the potential energy and kinetic energy of the object.
  • The unit for energy is the joule (J).
  • The Law of Conservation of Energy states that energy cannot be created or destroyed, but can only be changed from one form into another.
  • The Law of Conservation of Mechanical Energy states that the total mechanical energy of an isolated system remains constant.
  • The table below summarises the most important equations:
Weight F g = m · g
Equation of motion v f = v i + g t
Equation of motion Δ x = ( v i + v f ) 2 t
Equation of motion Δ x = v i t + 1 2 g t 2
Equation of motion v f 2 = v i 2 + 2 g Δ x
Potential Energy P E = m g h
Kinetic Energy K E = 1 2 m v 2
Mechanical Energy U = K E + P E

End of chapter exercises: gravity and mechanical energy

  1. Give one word/term for the following descriptions.
    1. The force with which the Earth attracts a body.
    2. The unit for energy.
    3. The movement of a body in the Earth's gravitational field when no other forces act on it.
    4. The sum of the potential and kinetic energy of a body.
    5. The amount of matter an object is made up of.
  2. Consider the situation where an apple falls from a tree. Indicate whether the following statements regarding this situation are TRUE or FALSE. Write only 'true' or 'false'. If the statement is false, write down the correct statement.
    1. The potential energy of the apple is a maximum when the apple lands on the ground.
    2. The kinetic energy remains constant throughout the motion.
    3. To calculate the potential energy of the apple we need the mass of the apple and the height of the tree.
    4. The mechanical energy is a maximum only at the beginning of the motion.
    5. The apple falls at an acceleration of 9,8 m · s - 2 .
  3. [IEB 2005/11 HG] Consider a ball dropped from a height of 1 m on Earth and an identical ball dropped from 1 m on the Moon. Assume both balls fall freely. The acceleration due to gravity on the Moon is one sixth that on Earth. In what way do the following compare when the ball is dropped on Earth and on the Moon.
    Mass Weight Increase in kinetic energy
    (a) the same the same the same
    (b) the same greater on Earth greater on Earth
    (c) the same greater on Earth the same
    (d) greater on Earth greater on Earth greater on Earth
  4. A man fires a rock out of a slingshot directly upward. The rock has an initial velocity of 15 m · s - 1 .
    1. How long will it take for the rock to reach its highest point?
    2. What is the maximum height that the rock will reach?
    3. Draw graphs to show how the potential energy, kinetic energy and mechanical energy of the rock changes as it moves to its highest point.
  5. A metal ball of mass 200 g is tied to a light string to make a pendulum. The ball is pulled to the side to a height (A), 10 cm above the lowest point of the swing (B). Air friction and the mass of the string can be ignored. The ball is let go to swing freely.
    1. Calculate the potential energy of the ball at point A.
    2. Calculate the kinetic energy of the ball at point B.
    3. What is the maximum velocity that the ball will reach during its motion?
  6. A truck of mass 1,2 tons is parked at the top of a hill, 150 m high. The truck driver lets the truck run freely down the hill to the bottom.
    1. What is the maximum velocity that the truck can achieve at the bottom of the hill?
    2. Will the truck achieve this velocity? Why/why not?
  7. A stone is dropped from a window, 3 m above the ground. The mass of the stone is 25 g .
    1. Use the Equations of Motion to calculate the velocity of the stone as it reaches the ground.
    2. Use the Principle of Conservation of Energy to prove that your answer in (a) is correct.

Questions & Answers

what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Maths test. OpenStax CNX. Feb 09, 2011 Download for free at http://cnx.org/content/col11236/1.2
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